Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1728 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1728 conjugacy classes of subgroups — too many to draw. Only its 557 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#15668450 | C2 | semidirect |
| 2. #26041830 | C2 | direct (N × H) |
| 3. C2×#19153813 | C2 | semidirect |
| 4. C2×#19153805 | C2 | semidirect |
| 5. C2×#19153791 | C2 | semidirect |
| 6. C2×#19153778 | C2 | semidirect |
| 7. C2×C42×D181 | C2 | semidirect |
| 8. C2×C4⋊Q8×C181 | C2 | semidirect |
| 10. C2×#15668450 | C22 | semidirect |
| 17. #19153813 | C22 | semidirect |
| 18. #19153805 | C22 | semidirect |
| 19. #19153791 | C22 | semidirect |
| 20. #19153778 | C22 | semidirect |
| 24. C42×D181 | C22 | semidirect |
| 26. C4⋊Q8×C181 | C22 | semidirect |
| 42. C2×C4×D181 | D4 | semidirect |
| 71. C4×D181 | C2×D4 | semidirect |
| 76. C2×C4×C181 | #41 | semidirect |
| 91. C4×C181 | C2×#41 | semidirect |
| 94. C2×C181 | #532 | semidirect |
| 99. C181 | C2×#532 | semidirect |
| 103. C2×C4⋊Q8 | D181 | semidirect |
| 118. C4⋊Q8 | C2×D181 | semidirect |
| 176. C2×C4 | #15668450 | semidirect |
| 193. C4 | C2×#15668450 | semidirect |
| 196. C2 | #26041830 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668450 | 2 |
| #26041830 | 2 |
| C2×#19153813 | 2 |
| C2×#19153805 | 2 |
| C2×#19153791 | 2 |
| C2×#19153778 | 2 |
| C2×C42×D181 | 2 |
| C2×C4⋊Q8×C181 | 2 |
| C2×#532 | 181 |